bonusProblems

Suppose you invest $1,000 in a volatile stock. Each year, with equal probability, it either rises 40% or falls by 30%. What would be the expected (in other words the mean) value of the stock after 50 years? What would be the most likely (in other words the median) value after that time? (hint: they are not the same).

6) Making Prunes

Before a plum is dried to make a prune, it is 92% water. A prune is just 20% water. If only water is evaporated in the process, how many pounds of prunes can be made from 100 pounds of plums?

7) Pet Preferences

Students were surveyed on their preference for pets. Three fourths of the students surveyed liked dogs, three fifths like cats, and one sixth did not like either. What is the fewest number of students surveyed that could like both cats and dogs?

8) Fluctuating Stock

If a stock that is currently worth $50 per share rises by 160% this year and then falls by 70% the next year. How much will it then be worth?

9) Spiders and Beetles

In a cage full of bugs, there are beetles (6 legs) and spiders (8 legs). There are 162 more legs than bugs, and 18 more beetles than spiders. How many spiders are there?

10) Birthday paradox

Suppose there are 23 students in Math League. What is the chance that two students share the same birthday?

11) Birthday paradox

How can you measure nine minutes using just 7 minute and 4 minute hour glasses without taking more than nine minutes?

12) Standing in Line

How many different ways can 6 friends stand in line if Alice and Bob refuse to stand next to each others?

13) Picking Cards

What is the probability that the top 4 cards drawn from a shuffled deck of 52 cards are all the same suit?

14) Selling Flour for Profit

A miller takes as toll one tenth of the flour that he grinds for a customer. How much did he grind for a customer who had only one kilogram after the toll had been taken?

15) Birthday paradox

A man lived one fourth of his life as a boy, one fifth as a youth, one third as a man in his prime, and thirteen years in old age. How long did he live?



	Bonus Problems (for 2011 - 2012 year)

	Here are the bonus problems that I have given so far this year. You can submit answers up to the time when I post the solution to the solutions page. You can discuss the problem with whoever you want, but answers must be submitted in your own handwriting. It is not enough to submit a number as your answer. A complete, comprehensible, explanation of how you solved it must be provided as well. 1) Chimps Bert and Alice Bert is twice as old as Alice was when Bert was as old as Alice is now. There combined age is 105. How old are they? 2) Collaborative Jigsaw Puzzle It takes Bert 4 hours to complete a jigsaw puzzle, but Alice can do it in 3 hours. How long would it take them if they worked together? 3) Crossing a Bridge Four people (Alice, Bert, Charlie, Diane) need to cross a bridge in the dark with only one flashlight. Only two can cross at a time. Alice can cross in 1 minute, Bert in 2, Charlie in 5, and Diane in 7 minutes. When a pair goes across they can only go as fast as the slower of the two. They have to catch a bus in 15 minutes. Can they make it? If so, how? 4) Roots What is the least integer N greater than 1 for which the square root of N, the cube root of N, and the fourth root of N are all integers? 5) Investing Suppose you invest $1,000 in a volatile stock. Each year, with equal probability, it either rises 40% or falls by 30%. What would be the expected (in other words the mean) value of the stock after 50 years? What would be the most likely (in other words the median) value after that time? (hint: they are not the same). 6) Making Prunes Before a plum is dried to make a prune, it is 92% water. A prune is just 20% water. If only water is evaporated in the process, how many pounds of prunes can be made from 100 pounds of plums? 7) Pet Preferences Students were surveyed on their preference for pets. Three fourths of the students surveyed liked dogs, three fifths like cats, and one sixth did not like either. What is the fewest number of students surveyed that could like both cats and dogs? 8) Fluctuating Stock If a stock that is currently worth $50 per share rises by 160% this year and then falls by 70% the next year. How much will it then be worth? 9) Spiders and Beetles In a cage full of bugs, there are beetles (6 legs) and spiders (8 legs). There are 162 more legs than bugs, and 18 more beetles than spiders. How many spiders are there? 10) Birthday paradox Suppose there are 23 students in Math League. What is the chance that two students share the same birthday? 11) Birthday paradox How can you measure nine minutes using just 7 minute and 4 minute hour glasses without taking more than nine minutes? 12) Standing in Line How many different ways can 6 friends stand in line if Alice and Bob refuse to stand next to each others? 13) Picking Cards What is the probability that the top 4 cards drawn from a shuffled deck of 52 cards are all the same suit? 14) Selling Flour for Profit A miller takes as toll one tenth of the flour that he grinds for a customer. How much did he grind for a customer who had only one kilogram after the toll had been taken? 15) Birthday paradox A man lived one fourth of his life as a boy, one fifth as a youth, one third as a man in his prime, and thirteen years in old age. How long did he live?